Question
In: Finance
Consider a four-year bond with a 10 percent coupon paid semiannually (or 5 percent paid every...
Consider a four-year bond with a 10 percent coupon paid semiannually (or 5 percent paid every 6 months) and an 8 percent rate of return (rb). Suppose that the rate of return increases by 10 basis points (1/10 of 1 percent) from 8 to 8.10 percent. Then, using the semiannual compounding version of the duration model shown above, how much is the percentage change in the bond's price?
Solutions
Expert Solution
| Statement showing price of bond: (assume face value to be $1000, in case of semiannual years to maturity will be 8 years, coupon payment= 1000*0.05=$50, yield is 4%) | ||||
| Particulars | Time | PVf @4% | Amount | PV |
| Cash Flows (Interest) | 1.00 | 0.9615 | 50.00 | 48.08 |
| Cash Flows (Interest) | 2.00 | 0.9246 | 50.00 | 46.23 |
| Cash Flows (Interest) | 3.00 | 0.8890 | 50.00 | 44.45 |
| Cash Flows (Interest) | 4.00 | 0.8548 | 50.00 | 42.74 |
| Cash Flows (Interest) | 5.00 | 0.8219 | 50.00 | 41.10 |
| Cash Flows (Interest) | 6.00 | 0.7903 | 50.00 | 39.52 |
| Cash Flows (Interest) | 7.00 | 0.7599 | 50.00 | 38.00 |
| Cash Flows (Interest) | 8.00 | 0.7307 | 50.00 | 36.53 |
| Cash flows (Maturity Amount) | 8.00 | 0.7307 | 1,000.00 | 730.70 |
| Current Bond Price | 1,067.34 | |||
| Price of bond= $1067.34 | ||||
| Statement showing price of bond: (assume face value to be $1000, in case of semiannual years to maturity will be 8 years, coupon payment= 1000*0.05=$50, yield is 4.05%) | ||||
| Particulars | Time | PVf @4.05% | Amount | PV |
| Cash Flows (Interest) | 1.00 | 0.9611 | 50.00 | 48.05 |
| Cash Flows (Interest) | 2.00 | 0.9237 | 50.00 | 46.18 |
| Cash Flows (Interest) | 3.00 | 0.8877 | 50.00 | 44.39 |
| Cash Flows (Interest) | 4.00 | 0.8532 | 50.00 | 42.66 |
| Cash Flows (Interest) | 5.00 | 0.8200 | 50.00 | 41.00 |
| Cash Flows (Interest) | 6.00 | 0.7880 | 50.00 | 39.40 |
| Cash Flows (Interest) | 7.00 | 0.7574 | 50.00 | 37.87 |
| Cash Flows (Interest) | 8.00 | 0.7279 | 50.00 | 36.39 |
| Cash flows (Maturity Amount) | 8.00 | 0.7279 | 1,000.00 | 727.90 |
| Current Bond Price | 1,063.84 | |||
| Price of bond= $1063.84 | ||||
| Percentage change in bond price=(1063.84-1067.34)/1067.34*100= -0.33% | ||||
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